Reentrant Canonical Spin-Glass Dynamics and Tunable Field-Induced Transitions in (GeMn)Co 2 O 4 Kagome lattice.

We report on the reentrant canonical semi spin-glass (SG) characteristics and controllable field-induced transitions in broken Kagomé symmetry of (GeMn)Co 2 O 4 . This B -site spinel exhibits complicated magnetic behavior in which the longitudinal ferrimagnetic (FiM) order sets in below the Néel temperature T FN ~77 K due to uneven moments of Co 2+ (↑ 5.33 μ B ) and Mn 4+ (↓ 3.87 μ B ) which coexists with transverse SG state below 72.85 K. Such complicated magnetic behavior results from the competing anisotropic superexchange interactions ( J AB / k B ~ 4.3 K, J AA / k B ~ -6.2 K and J BB / k B ~ -3.3 K) between the cations, which is extracted following the Néel's expression for the two-sublattice model. Dynamical susceptibility (χ ac ( f, T )) and thermoremanent magnetization M TRM ( t ) data analysed by means of the empirical scaling-laws: Vogel-Fulcher law and Power law of critical slowing down, reveal the reentrant SG like character which evolves through several metastable states. The magnitude of Mydosh parameter (Ω~0.002), critical exponent zν =(6.7±0.07), spin relaxation time τ 0 =(2.33±0.1)×10 -18 s, activation energy E a / k B =(69.8±0.95) K and interparticle interaction strength ( T 0 =71.6 K) provide the experimental evidences for canonical SG state below the spin freezing temperature T F =72.85 K. Isothermal magnetization plots reveal two field-induced transitions across 9.52 kOe ( H SF1 ) and 45.6 kOe ( H SF2 ) associated with the FiM domains and spin-flip transition, respectively. Analysis of the inverse paramagnetic susceptibility χ p -1 (χ p =χ-χ 0 ) after subtracting the temperature independent diamagnetic term χ 0 (= -3×10 -3 emu mol -1 Oe -1 ) results in the effective magnetic moment μ eff =7.654 μ B / f.u. This agrees well with the theoretically obtained μ eff =7.58 μ B / f.u. resulting in the cation distribution (Mn 0.2 4+ ↓) A [Co 2 2+ ↑] B O 4 in support of the Hund's ground state spin configuration S =3⁄2 and S =1⁄2 of Mn 4+ and Co 2+ , respectively. The H-T phase diagram established by analysing all the parameters ( T F ( H ), T FN ( H) , H SF1 ( T ) and H SF2 ( T )) extracted from various magnetization measurements enables clear differentiation among the different phases of (GeMn)Co 2 O 4 .